The aim is to optimize prototypes representing 'average'
vectors for each class, that is, a class-related cluster
structure of the data cloud is assumed.

Here, the extension of Hammer & Villmann (2002) for learning
weights (relevances) of the squared Euclidean data metric along
with the prototypes, called GRLVQ, is provided.
Also a version for learning metrics relevances expressed by
quadratic matrix forms similar to MRLVQ by Schneider, Biehl and Hammer(2009).
Metric adaptation can help reduce the curse of dimensionality for
high-dimensional data.

Contrary to existing algorithms, this package provides a
2nd order batch optimization (l-BFGS) for the learning,
which -in addition with a steep discriminative function- allows
much faster and somewhat more accurate calculations than obtained
by standard stochastic gradient descent optimization.

For Euclidean metrics, GRLVQ was shown by Hammer, Strickert, and
Villmann (2005) to be a large margin optimizer in the
flavour of support vector machines, but with compact and
interpretable class representatives living in the data space.
In the limit of step discriminative functions, the
cost function directly minimizes misclassification.

For practical use just define the desired number of
prototypes per class. You can adjust the convergence goals
on demand. In matrix learning you can specify the dimension
of the subspace, that is, the rank n_vec of the quadratic matrix
form.